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Evaluate
∑n=1,3,5,7....∞e(2n−1)∫0n+1xeex(x+1)!dx \Large{\sum _{ n=1,3,5,7.... }^{ \infty }{ \frac { { e }^{ \left( 2n-1 \right) } }{ \int _{ 0 }^{ n+1 }{ \frac { { x }^{ e }{ e }^{ x } }{ \left( x+1 \right) ! } dx } } } }n=1,3,5,7....∑∞∫0n+1(x+1)!xeexdxe(2n−1)
Note by Department 8 5 years, 3 months ago
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2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
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@Tanishq Varshney,@Otto Bretscher,@Brian Charlesworth,@Michael Mendrin,@Aditya Kumar
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@Jake Lai
Very unlikely this series has a closed form. Factorials/gamma functions in integrals, especially in denominators of integrals, are difficult to evaluate in general.
It is best to proceed in the direction of a motivating problem which applies integration in its solution, or to build a problem on the back of techniques already well-studied.
@Jake Lai – I made it accidently
@Pi Han Goh
What have you tried? What makes you think there's a closed form?
I don't know I just made this problem and asked my school teacher, she said it was pretty tough. So I asked for help.
Not all series /integrals has a nice closed form.
@Pi Han Goh – Sorry
@Pi Han Goh – try this
@Department 8 – See the report. Your problem is flawed.
I'm currently busy now. Ty using the infinite product of gamma(x+2)
@Jonas Katona
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Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.
When posting on Brilliant:
*italics*
or_italics_
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or__bold__
paragraph 1
paragraph 2
[example link](https://brilliant.org)
> This is a quote
\(
...\)
or\[
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to ensure proper formatting.2 \times 3
2^{34}
a_{i-1}
\frac{2}{3}
\sqrt{2}
\sum_{i=1}^3
\sin \theta
\boxed{123}
Comments
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Top Newest@Tanishq Varshney,@Otto Bretscher,@Brian Charlesworth,@Michael Mendrin,@Aditya Kumar
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@Jake Lai
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Very unlikely this series has a closed form. Factorials/gamma functions in integrals, especially in denominators of integrals, are difficult to evaluate in general.
It is best to proceed in the direction of a motivating problem which applies integration in its solution, or to build a problem on the back of techniques already well-studied.
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@Pi Han Goh
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What have you tried? What makes you think there's a closed form?
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I don't know I just made this problem and asked my school teacher, she said it was pretty tough. So I asked for help.
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Not all series /integrals has a nice closed form.
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this
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I'm currently busy now. Ty using the infinite product of gamma(x+2)
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@Jonas Katona
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